Full text: Musschenbroek, Petrus: Physicae experimentales, et geometricae de magnete, tuborum capillarium vitreorumque speculorum attractione, magnitudine terrae, cohaerentia corporum firmorum dissertationes

515. PROPOSITIO XXXVII.

Tab. XIX. fig. 4. Potentiæ frangentes applicatæ extremitati-
bus duorum Cylindrorum A B C D, E F P, ejusdem materiæ, ſed
longitudine & craſſitie diverſorum, ſunt in ratione compoſita ex
triplicata diametrorum baſium A B, E F. & inverſa longitudi-
num A D, E P. ſepoſita corporum gravitate.

Eſt Cohærentia baſeos A K B L, ad Cohærentiam baſeos E M F O,
in ratione triplicata diametri A B ad E F per Propoſ. XXXVI. ad-
eoque poſitis Cylindris B Q, F P æque longis, erunt potentiæ fran-
gentes in Q & P, in ratione triplicata diametrorum A B, E F, ſed
potentia in Q eſt ad eam in D frangentem, uti A D ad A Q per
Prop. X X. Quare erit potentia frangens in D, ad eam in P Cy-
lindri F P, in ratione compoſita ex triplicata A B ad E F, & A Q
= E P ad A D.

516. PROPOSITIO XXXVIII.

Tab XXIII. fig. 37. Duo Cylindri ſimiles A B C D, E F G H
ejusdem materiæ, horizontaliter parieti infixi, ſuſtinere poſſunt
ab extremitatibus D & H, pondera I & K quæ ſunt baſibus propor-
tionalia ſepoſitâ Cylindrorum gravitate.

Eſt Cohærentia Cylindri A B C D, ad Cohærentiam Cylindri
E F G H, uti cubus diametri A B ad cubum diametri E F per Prop. XXXVI. ſed quia Cylindri ſunt ſimiles, eſt A B, E F: : A D. E H. ergo AB c , EF c : : AD c , EH c . unde erunt Cohærentiæ cylindro-
rum uti AD c , ad EH c . Eſt vero momentum ponderis I = I X
A D. quod eſt æquale Cohærentiæ baſeos, ſive = AD c . adeoque
utrimque facta diviſione per A D, erit I = AD q . eodem modo pon-
deris K momentum eſt = K X E H. & Cohærentia, cui æquale
eſſe debet, eſt = EH c . quareutrimque facta diviſioneper E H, erit
K = EH q . erit igitur pondus I ad pondusK: : AD q . E H q : : A B q . EF q : :
baſis A B S ad baſin E F R. adeoque pondera ſunt baſibus proportio-
nalia.

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